FIRST PUBLICATION OF THE "BERNOULLI EQUATION".

LEIBNITII, GODOFREDI GUILIELMI. (GOTTFRIED WILHELM LEIBNIZ) & BERNOULLII (IACOBI). (JACOB BERNOULLI) & BERNOULLII (IOHANNIS). (JOHANN BERNOULLI).

Specimen Dynamicum (+) Notatiuncula Constructiones Lineae in qua Sacoma aequilibrium cum pondere moto faciens incedere debet. Et quaedam de Quadraturis (+) Resposio ad nonnullas Difficultates a Bern. Nieuwentüt circa Methodum differentialem motas (+) Additio ad hoc Schediasma (+) De novo usu centri gravitatis ad dimensiones: ubi et de Parallelis in Universum [Five papers by Leibniz]. Explicationes, Annotationes et Additiones ad ea, quae in Actis sup. anni de Curva Elasitica, Isochrona Paracentrica et Velaria leguntur et c. (+) Solutiones Problematis Physico-Mathematici. [Two papers by Jacob Bernoulli]. Demonstratio Identitatis Curvae Aequilibrationis cum Cycloide et c. (+) Meditatio de Dimensione linearum curvarum per circulares. [Two papers by Johann Bernoulli].

Leipzig, Grosse & Gleditsch, 1695. 4to. Contemp. full vellum. Faint handwritten title on spine. A small stamp on titlepage and pasted library label to pasted down front free end-paper. In: "Acta Eruditorum Anno MDCXCV". (2), 560, (52) pp. + 10 plates. As usual with various browning to leaves and plates. The entire volume offered. Leibniz's papers: pp. 145-57; 184-185; 310-316; 369-372; 493-495. Jacob Bernoulli's paper: pp. 537-553 + one folding table; 65-66. Johann Bernoulli's: pp. 59-65; 374-376.

First printing of a series of influential papers by Leibniz, Jacob Bernoulli and Johann Bernoulli.

First publication of Jakob Bernoulli's famous and influential "Bernoulli Equation".
In "Notatiuncula Constructiones Lineae" Bernoulli proposed a solution to non linear equations which today is one of the most common used solutions of the general fluid. Bernoulli equations are significant because they are nonlinear differential equations with known exact solutions.
In the "Specimen dynamicum" Leibniz presents a conception of body and force which distinct between primitive and derivative forces and between active and passive forces. This article is regarded as being the clearest exposition of Leibniz' dynamics. (DSB VII, 151b).

"The first attempt at a detailed account of the dynamics was a long dialogue, the "Phoranomus seu de potentia et legibus naturae," written in July 1689 while Leibniz was in Rome. This was quickly followed be the composition of the massive Dynamica de potential et legibus naturae corporeae (1689-90) [...]. Though it was written with the intention of publication, and though Leibniz work at publishing it, he never considered it entirely finished and it remained unpublished during his lifetime.
The later [...] he finally revealed some of the metaphysical foundations of the project in an essay [the present paper]." (Garber, Daniel. Leibniz: body, substance, monad. 2009. 132 p.)

"Its title suggests a summary of or a selection from the earlier work [...]. However, it actually contains something in a way rather more interesting: a careful exposition of the metaphysical foundations of the new science, something that is hard to find in the old Dynamica or any of the more Technical pieces." (Garber, Daniel. Leibniz: Body, Substance, Monad. 2009. 133 p.)

Order-nr.: 42860